1 Consider a spherical planet which is rotating about its axis such that the speed of a point on its equator is v and the effective acceleration due to gravity on the equator is $\frac{1}{3}$ of its value at the poles. What is the escape velocity for a particular at the pole of this planet A) 3 v B) 2 v C) $\sqrt{3}$ v D) $\sqrt{2}$ v
2 For the circuits A and B as shown in the figure, identify the correct option A) Circuit A is for accurate measurement of high resistance and B is for low resistance B) Circuit A is for accurate measurement of low resistance and B is for high resistance C) Both circuits can accurately measured high resistance only D) Both circuits can accurately measured low resistance only
3 An electromagnetic wave of frequency 3.0 MHz passes from vacuum into a non-magnetic medium with permittivity, $\epsilon=16 \epsilon_{0}$ . where $ \epsilon_{0}$ is the free space permittivity. The change in wavelength is A) -75 m B) +75 m C) -50 m D) +50 m
4 The collision of an electron with kinetic energy 5.5 eV and a hydrogen atom in its ground state can be described as A) completely inelastic B) may be completely inelastic C) may be partially elastic D) elastic
5 A particle of mass m is moving along a circle of radius R such that its tangential acceleration at varies with distance covered x as at =ax2 where $\alpha$ is a constant. The kinetic energy,K of the particle varies with the distance as K= $\beta x^{c}$, where $\beta$ and c are constants. The values of $\beta$ and c are A) $\beta=\frac{m\alpha}{3};c=3$ B) $\beta=\frac{m\alpha}{4};c=3$ C) $\beta=\frac{m\alpha}{2};c=3$ D) $\beta=\frac{m\alpha}{2};c=3$
6 Statement A Convection involves the flow of matter within a fluid due to unequal temperature of its parts Statement B A hot bar placed under a running tap water loses heat due to the effect of convection with in water Statement C Heat transfer always involves temperature different between two systems. Identify the correct option A) A, B, C are true B) Only A and C are true C) Only A and B are true D) Only B and C are true
7 An ideal gas is placed in a tank at $27^{0} C$. The pressure is initially 600 kPa. One-fourth of the gas is then released from the tank and thermal equilibrium is established. What will be the pressure if the temperature is $327^{0}$ C? A) 900 kPa B) 1000 kPa C) 1050 kPa D) 1250 kPa
8 Find the potential difference between a and b as shown in the below circuit A) 165 V B) 198 V C) 213 V D) 224 V
9 A particle A moves along the line, y=30m with a constant velocity, v parallel to the x-axis. At the momemt particle A passes the y-axis, particle B starts from the origin witrh zero initial speed and a constant acceleration .$a=0.40 m/sec^{2}$ . The angle between a and y-axis is $60^{0}$. If the particles A and B collide after sometimes , then the value of |v| will be A) 2 m/s B) 3 m/s C) 4 m/s D) 5 m/s
10 A rocket motor consumes 100 kg of fuel per second exhausting it with a speed of 5 km/s. The speed of the rocket when its mass is reduced to $\frac{1}{20}^{th}$ of its initial mass, is [Assume initial speed to be zero and ignored gravitational and viscous forces] A) 20 km/s B) 40 in (2) km/s C) 5 in (20) km/s D) 10 in (10) km/s
11 A water tank kept on the ground has an orifice of 2 mm diameter on the vertical side. What is the minimum height of the water above the orifice for which the output flow of water is found to be turbulent? [ Assume g=10 m/s2, $\rho_{water}$= 103 kg/m3, viscosity =1 centi-poise] A) 3 cm B) 4 cm C) 6 cm D) 2 cm
12 A carnot engine with efficiency $\eta$ operates between two heat reservoirs with temperatures $T_{1}$ and $T_{2}$ , where $T_{1} >T_{2}$ . If only $T_{1}$ is changed by 0.4% , the change in efficiency is $\triangle\eta_{1}$ , whereas if only $T_{2}$ is changed by 0.2% , the efficiency is changed by $\triangle\eta_{2}$ . The ratio $\frac{\triangle\eta_{1}}{\triangle\eta_{2}}$ is approximately A) -2 B) -4 C) +3 D) +4
13 A drone fitted with siren in flying directly away from the drone operator and towards a distant building at a speed of 15 m/s . The siren produces the sound of frequency 780Hz. What is the frequency that the operator hears in the echo refected from the building,[ speed of sound is 340 m/s] A) 766 Hz B) 800 Hz C) 816Hz D) 840Hz
14 For the circuit shown in the figure, calculate the resistance between points A and B A) 0.5 R B) R C) 15 R D) $\frac{6}{5}R$
15 A current carrying conductor obeys Ohm's law (V= RI). If the current passing through the conductor is $l=(5\pm0.2)$A and voltage developed is $V=(60\pm6)$ V , then find the percentage of error is resistance, R A) 18 B) 6 C) 14 D) 2